Mathematical models are used to elucidate properties of the monomer-monomer and monomer-dimer type chemical reactions on a two-dimensional surface. We use mean-field and lattice gas models, detailing similarities and differences due to correlations in the lattice gas model;The monomer-monomer, or AB surface reaction model, with no diffusion, is investigated for various reaction rates k. Study of the exact rate equations reveals that poisoning always occurs if the adsorption rates of the reactants are unequal. If the adsorption rates of the reactants are equal, simulations show slow poisoning, associated with clustering of reactants. This behavior is also shown for the two-dimensional voter model. We analyze precisely the slow poisoning kinetics by an analytic treatment for the AB reaction with infinitesimal reaction rate, and by direct comparison with the voter model. We extend the results to incorporate the effects of place-exchange diffusion, and we compare the AB reaction with infinitesimal reaction rate and no diffusion to the voter model with diffusion at rate 1[over]2. We also consider the relationship of the voter model to the monomer-dimer model, and investigate the latter model for small reaction rates;The monomer-dimer, or AB[subscript]2 surface reaction model is also investigated. Specifically, we consider the ZGB-model for CO-oxidation, and in generalizations of this model which include adspecies diffusion. A theory of nucleation to describe properties of non-equilibrium first-order transitions, specifically the evolution between 'reactive' steady states and trivial adsorbing states, is derived. The behavior of the 'epidemic' survival probability, P[subscript]s, for a non-poisoned patch surrounded by a poisoned background is determined below the poisoning transition. Both the characteristic or 'critical' patch size, and the sharpness of the increase of P[subscript]s with size are shown to increase as the transition is approached, and also as diffusion increases. This behavior is further elucidated by investigation of the propagation of an interface separating reactive and poisoned phases, and of appropriate reaction-diffusion equations for the regime of high diffusion.